Two wonderful trigonometric identities (Q2730647)
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scientific article; zbMATH DE number 1631468
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two wonderful trigonometric identities |
scientific article; zbMATH DE number 1631468 |
Statements
8 August 2001
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generating function
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trigonometric identities
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Two wonderful trigonometric identities (English)
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The author proves two identities: NEWLINE\[NEWLINE4^{n}\prod ^{n}_{i=1}\left( \cos \frac{\pi i}{2n+1}\right) ^{2}=1,\;\;\;4^{n}\prod ^{n}_{i=1}\left( \cos \frac{\pi i}{2n+2}\right) ^{2}=n+1,NEWLINE\]NEWLINE where \( n\in \left\{ 1,2,\ldots \right\}\). The proof is based on the generating function approach.
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